Step 1: Concept
Write the formula for the equation of a line in terms of point-slope form
and in slope-intercept form.
[tex]\begin{gathered} Pi\text{ont slope form is given below} \\ y-y_1=m(x-x_1) \\ \text{Slope}-\text{intercept form} \\ y\text{ = mx + c} \\ m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \end{gathered}[/tex]Where
m = slope
c = intercept
Step 2: Represent the coordinates
[tex]\begin{gathered} (x_1,y_1\text{ ) = (1, -5)} \\ (x_2,y_2\text{ ) = ( -3, 7)} \end{gathered}[/tex]Step 3: Find the slope, using slope formula.
[tex]\begin{gathered} m\text{ = slope} \\ \text{m = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = }\frac{7\text{ -(-5)}}{-3\text{ -1}} \\ m\text{ = }\frac{7\text{ + 5}}{-4} \\ m\text{ = }\frac{12}{-4} \\ m\text{ = -3} \end{gathered}[/tex]Step 4: Write an equation for the line in point-slope form.
[tex]\begin{gathered} \text{y - y}_1=m(x-x_1) \\ y\text{ -(-5) = -3(x - 1)} \\ \text{y + 5 = -3(x - 1)} \end{gathered}[/tex]Step 5: Simplify the equation in 4 to write the equation in slope-intercept form.
y + 5 = -3(x - 1)
y + 5 = -3x + 3
y = -3x + 3 - 5
y = -3x - 2
Final answer
Option B
y + 5 = -3(x - 1)
y = -3x - 2